Starter cards can mean any number of things, for example, a store card only good at that specific store/website, a gas card, a secured major credit card (Mastercard, Visa), a student card with a very low initial credit limit, and so on.
Each card will have its own criteria for deciding who gets approved, and for how much.
You mentioned that you're rebuilding, and have a 2-year credit history. If you'd give us more details, we might be able to suggest specific cards that have a good chance of approval. Why are you rebuilding--was there a bankruptcy? charge-offs? collections? What credit do you currently have? And where are they in the two year time-frame?
Welcome to the forums and I applaud your courage and progress on starting a new life! I know that is difficult!
you have plenty of credit cards now so you shouldn't take out cards just to pad utilization. It will appear as credit seeking... especially if your goal is to get secured cards with Citi and Discover. New cards lowers the age of your accounts and the inquiries (assuming that they do them) also will look bad.
Do have a parent or grandparent (even if they are deceased) that was in the military? If so, you qualify for Navy Federal Credit Union membership and that should be your next step.
Discover also has a prequalification site that will tell you whether you would be approved without the hard pull. Finally, if you are on the east coast, you would also probably qualify for TD Bank's secured card.
If you focus on the bigger banks or credit unions where you can build history, you'll quickly move past starter cards and into mainstream cards that you'll use and keep for years to come.
Im sure others will chime in but wanted to start you out with my thoughts.
FWIW, it sounds like you are off to a good start based on the prequals you are getting. Now focus on mainstream lenders to continue your build!
Good luck!
ETA: you only need 3 credit cards and 1 installment loan for optimal Fico scoring. There is a lot of misinformation on YouTube... your best bet is to hang out here, ask questions and listen to those who have successfully done rebuilds. You'll get information that is directly relevant to YOUR profile and not aimed at getting eyeballs and ad impressions!
@Anonymous
One more thing... assuming you have had your overstock card for 6 weeks or more, try logging into your account and ask for a credit limit increase (CLI) and you migh bet a large one which will help your overall utilization and will only be a soft pull.
I got my Overstock in January with a starting limit of 600 bucks... that was doubled in February. Now it is up to 4700.00. You ask for a CLI every 61 days and it will grow. Even set reminders on your calendar to keep track and continue to grow the cards.
@Anonymous wrote:Thank you so much! I'll follow this advice!
A few additional comments:
- I grew up in a household with an abusive and horribly controlling stepfather and watched my mom do what it took to get us out from underneath his extensive reach; I applaud your courage to getting out and restarting.
- If you are not able to join Navy Federal, you can almost certainly join PenFed; you already have enough credit cards for optimal FICO scoring, but unless I missed it, you don't have an installment loan (car, mortgage, or signature loan), and both Navy Federal and PenFed can help you there by allowing you to open up a Secured Share Loan (SSL).
@Anonymous wrote:Thank you, I will definitely look into the secured share loan. I have an installment loan from a Self Credit Builder account but would be happy to do more research on the subject.
I am unfamiliar with the Self account, that may do the trick depending upon how it reports. 
You dont need a SSL if you have a Self loan.... may want to switch to a SSL at some point after the self loan is over though..
-J
